Graham Beasley

2022-07-16

Consider a matrix $X\in {\mathbb{R}}_{n×m}$
One compact yet unclear notation to select a row or column from this matrix is:
$x\in X$
How do you clearly select a row or column from a matrix?
I know $X=\left({x}_{ij}\right)$ is a standard notation to select elements. Though I haven't seen this used, ${x}_{i}\in {X}_{ij}$ for rows and ${x}_{j}\in {X}_{ij}$ for columns might make sense. This is motivated by a similar notation I have seen, namely $\sum _{i}{X}_{ij}$ for row sum or $\sum _{j}{X}_{ij}$ for column sum.

dasse9

Expert

You could for example use elementary vectors. Let ${e}_{j}$ be an $m×1$ vector of zeros with a one in j-th position. Then
${x}_{j}=X{e}_{j}$
would be the j-th column of X.

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Recalculate according to your conditions!